Question

In the figure given below, AC = AD. Choose the correct relation between AB and AD.

• A. AB > BD
• B. AB = BD
• C. AB < BD
• D. Cannot be determined

Answer 1

The correct option is A AB > BD


In $\Delta ABC$ and $\Delta ACD$,
$\angle 1=\angle 3+\angle 4$ [Exterior angle property of a triangle]
But $\angle 1=\angle 2$ ($\because AC=AD$ and angles opposite to equal sides are equal)
$\Rightarrow \angle 2=\angle 3+\angle 4$
$\Rightarrow \angle 2>\angle 3$
Hence, $AB>AD$. [Side opposite to greater angle is larger as compared to smaller angle]